Speaking about infinitely growing patterns, is such a pattern as a stationary wickstretcher known? It would relate to a gun in the same way as a normal wickstretcher relates to a puffer. Are growing wicks known?

And hereby I mean wicks that are "reasonably closely connected", citing Jason Summers (otherwise the answer would be too easy).

codeholic wrote:Speaking about infinitely growing patterns, is such a pattern as a stationary wickstretcher known? It would relate to a gun in the same way as a normal wickstretcher relates to a puffer. Are growing wicks known?

To make the analogy complete, you'd need a wick that could grow into empty space without any support. I can't think of any such things offhand. Wicks generally need to be capped by (moving) wickstretchers. Otherwise they're probably just extensible spaceships in disguise.

There are certainly lots of wicks that need a moving wickstretcher end and a stationary end. -- In which case I seem to recall the stationary end is called a "post", but strangely the Life Lexicon and LifeWiki don't seem to have any confirmation for that.

codeholic wrote:Yes, that's what I meant. In some sense, such a wick would be a unidirectional replicator (it would replicate itself but only on one end).

EDIT: Alternatively, there might be a pattern, that makes a "wave" propagating through a wick and elongating it on the other end.

It HAS to be "pulses". If it is a 1D replicatior, well, OK, we could get easily a support... but we would need to find it first. And no such object has ever been seen.Pulses can be gliders, like in the pattern I threw, but it seems like a lazy solution.

This is game of life, this is game of life!Loafin' ships eaten with a knife!

If a stationary end stabilization can be found for the wick found stabilized in 114P6H1V0, then I think that could be considered a stationary wickstretcher. But such a stabilization would probably be very difficult to make.

codeholic wrote:EDIT: Alternatively, there might be a pattern, that makes a "wave" propagating through a wick and elongating it on the other end.

For that option, I think the best (only?) example in Conway's Life is Jason Summers' traffic-jam extruder (in Golly's Signal-Circuitry collection). Use goto.py to run it forward to a relatively interesting moment, say T=9576000. Then maybe watch it run in LifeHistory to see what's going on. One of the long "wick-pushing" reactions occurs just before T=9604000.

I think this almost counts -- the traffic lights are "reasonably closely connected" enough to sustain the traffic-jam chain reaction, anyway. But it takes some impressive circuitry to sustain the ever-slower movement of the far end of the wick.

dvgrn wrote:For that option, I think the best (only?) example in Conway's Life is Jason Summers' traffic-jam extruder (in Golly's Signal-Circuitry collection). Use goto.py to run it forward to a relatively interesting moment, say T=9576000. Then maybe watch it run in LifeHistory to see what's going on. One of the long "wick-pushing" reactions occurs just before T=9604000.

I think this almost counts -- the traffic lights are "reasonably closely connected" enough to sustain the traffic-jam chain reaction, anyway. But it takes some impressive circuitry to sustain the ever-slower movement of the far end of the wick.

... but 99,9999% of the time, the traffic lights aren't spaced enough. At almost any moment, you can zoom and see some non-jammed TLs. So, I don't think we can call this a wick. Especially since the inputs aren't regular.

This is game of life, this is game of life!Loafin' ships eaten with a knife!

Thanks in return for reminding me about it...! It took me most of a day to remember that the pattern even existed, and I had completely forgotten that I had checked it into Golly's pattern collection.

I don't think there are many other known "push" reactions that can do anything even vaguely equivalent. There's almost a way to use a pre-beehive to push a beehive, but it doesn't seem to be possible to chain those reactions cleanly.

Actually there exists a non-zero number k such that if you pick any location on the line of traffic lights, the traffic lights are eventually jammed a fraction of the time that is greater then k, so I think it qualifies as a wick.By the way, why do the reactions have to occur at such long intervals?

Kiran wrote:By the way, why do the reactions have to occur at such long intervals?

The reactions don't need the time they're given. However, the TL chain moves around, so there need to be a large number of options to match the possible locations of the first TL. The circuitry to deduce the proper *WSS salvo takes the time (although could likely be improved with current glider manipulation).

However, the *WSS salvo is able to communicate the termination of a pullback sequence, while this one just gets stuck. I feel like there's a glider salvo that can function the same though, and from it stable circuitry that cuts the pattern's bulk down considerably.

Edit: So I've decided I want to try my hand at making a TL extruder with some semblance of current technology (also just for the sake of making a thing to my liking). Do the construction-savvy have on hand a G salvo + Block that produces a 90 degree G without moving the block? I know it can be done with a 3G pushing elbow and 2G pull, but 5G seems excessive.

I have a good idea, but it isn't it Life. Very possibly there is a way to put together two HighLife c/98 spaceships in a line such that they interact in some generations. A gun producing the synthesis of the spaceship could extend the trail, so it would be a wickstretcher.

BlinkerSpawn wrote:Does the wick have to be anchored? If not, one could create a slide gun to repeatedly tack units onto the front of the above "wick".

First of all, a slidegun, in my opinion, can be only marginally qualified as a stationary pattern. Secondly, such patterns have already been built, see Life/Miscellaneous/tubstretch-c124b.rle by Jason Summers (that one makes a stationary pattern grow). But yes, it would be an interesting thing to build. Can anyone come up with a synthesis for the 114P6H1V0 pushalong?

gameoflifeboy wrote:I have a good idea, but it isn't it Life. Very possibly there is a way to put together two HighLife c/98 spaceships in a line such that they interact in some generations. A gun producing the synthesis of the spaceship could extend the trail, so it would be a wickstretcher.

That would be cheating. A c/98 spaceship can move autonomously and doesn't need a fencepost.

Can such a thing be described formally/mathematically?Edit: oh, puffer: wickstretcher = gun: stationary wickstretcher... Okay... That was enough for me to get that your criteria is sound enough and not made up of arbitrary rules.But!!! The wickstretcher in this analogy is a very strict one; one without any stationary support. (I think the TL extender and the QB extender in jslife qualifies.)

Hehe please let me elaborate I am pretty sure the first wickstretcher counts as a wickstretcher:wickstretcher 1Moving pattern, tight periodic product.Note that the periodic product is supported by a stationary part, and the term "wickstretcher" does not require the wick(tight periodic product) to be self-suatainable.

Now let's think about X in the analogy.Stationary factory, tight periodic product.And if we follow the analogy as is, the wick(tight periodic product) need not be self sustainable. Thus the following pattern,

Now, the term you should have put instead of "wickstretchers" in the analogy should be a subset of wickstretchers; i.e. wickstretchers that has no stationary part supporting the wick. (I'll call this subset 'Y' later.) The only examples I could find are tub/boatstretchers. Traffic jam stretchers and qb stretchers almost qualify (and may qualify if we tweak it a bit)

If you require the moving part of the wickstretcher to be nonempty when you define the term wickstretcher, interesting things happen. <s>cp4space</s>Y are the only wickstrerchers that don't qualify as X. And "stationary wickstretchers" are the only subset of X that don't qualify as wickstretchers